Horsepower and Torque Calculator
Engine power from torque and rpm, the torque from power and rpm, or the rpm from power and torque, in horsepower, metric horsepower, kW, lb·ft and N·m.
Result…
How it's calculated
Power (hp) = torque (lb·ft) × rpm ÷ 5252 (exactly 33 000 ÷ 2π) Power (kW) = torque (N·m) × rpm ÷ 9549.3 (exactly 60 000 ÷ 2π) Torque = power × constant ÷ rpm · RPM = power × constant ÷ torque 1 hp = 745.69987 W · 1 PS = 735.49875 W · 1 lb·ft = 1.3558179 N·m
Power is torque times rotational speed: P = T × ω, with ω = 2π × rpm ÷ 60 radians per second. In imperial units one horsepower is 550 foot-pounds-force per second, or 33 000 per minute, so hp = lb·ft × rpm ÷ (33 000 ÷ 2π) = lb·ft × rpm ÷ 5252. That is why power and torque curves cross at 5252 rpm when drawn in hp and lb·ft. In metric units kW = N·m × rpm ÷ 9549.3. The factors come from the exact international foot (0.3048 m), pound (0.45359237 kg) and standard gravity (9.80665 m/s²), as listed by NIST: 1 hp = 745.69987 W, 1 PS (metric horsepower) = 75 kgf·m/s = 735.49875 W, and 1 lb·ft = 1.3558179 N·m.
Your numbers, step by step
About the Horsepower and Torque calculator
This horsepower and torque calculator turns an engine's torque and rpm into power, or works backwards to the torque from power and rpm, or the rpm at which a given power and torque meet. Choose imperial to work in lb·ft and horsepower, or metric for N·m and kW; either way it shows the answer in every unit, including metric horsepower (PS), which is a little smaller than the mechanical horsepower used in the US and UK. It helps when reading a dyno sheet, comparing engines quoted in different countries, sizing an electric motor, or checking a spec sheet that gives torque but not power. The working is shown step by step from the exact definitions, and a chart draws the torque that would give the same power across the rev range, with your engine speed marked.
How to use it
- Choose what to “Work out”: Power, Torque or RPM.
- Pick “Units”: imperial for lb·ft and hp, metric for N·m and kW.
- Enter the two values you know: “Torque”, “Power” or “Engine speed”.
- Read the answer, then the other units below it, including metric horsepower (PS).
Worked example
An engine makes 350 N·m at 4,500 rpm. Power = 350 × 4,500 ÷ 9,549.3 = 164.93 kW. In watts that is 164,934 W, which is 164,934 ÷ 745.7 = 221.18 hp (mechanical) or 164,934 ÷ 735.5 = 224.25 PS (metric). The torque is 350 ÷ 1.3558 = 258.15 lb·ft.
Updated
Questions people ask
How do I convert torque to horsepower?
Multiply the torque in lb·ft by the rpm and divide by 5,252. In metric units, multiply N·m by rpm and divide by 9,549.3 to get kW.
Where does the number 5252 come from?
One horsepower is 550 foot-pounds-force per second, or 33,000 per minute. Power is torque times angular speed, and one revolution is 2π radians, so hp = lb·ft × rpm ÷ (33,000 ÷ 2π), and 33,000 ÷ 2π is 5,252.1. That is also why hp and lb·ft curves cross at 5,252 rpm.
What is the difference between hp and PS?
Mechanical horsepower (hp) is 745.7 W; metric horsepower (PS, CV or ch) is 735.5 W. The same engine therefore has about 1.4% more PS than hp. The factors are listed in the NIST Guide to the SI, Appendix B.9.
Is a common mistake mixing lb·ft and N·m?
Yes. Using N·m with the 5,252 constant overstates horsepower by about 36%. Pick the matching unit system, or let the calculator convert: 1 lb·ft = 1.3558 N·m.
Why is my car's measured power lower than the brochure figure?
Brochure figures are usually measured at the crankshaft, while a chassis dyno measures at the wheels after the gearbox and drivetrain have taken their share. The formula itself is exact; the inputs decide how close the answer is. The torque calculator works out torque from a force and lever arm.